In recent years, a travel assist apparatus which controls travel of a vehicle according to a set target has been under development. As one example of such a travel assist apparatus, there is known an apparatus that performs vehicle control such that the distance between two vehicles, that is, a host vehicle and a preceding vehicle present ahead of the host vehicle in the traveling direction of the host vehicle, is kept at a predetermined distance or more (refer to Patent Document 1, for example).
In the above-described apparatus, the distance between the host vehicle and the preceding vehicle is monitored. Then, when the distance between the two vehicles is less than a predetermined distance, a difference is calculated by subtracting the distance between the two vehicles from the predetermined distance, thereby controlling the vehicle speed (more specifically, a relative speed of the host vehicle with reference to the preceding vehicle) such that the difference becomes less than 0 (zero). For example, a target relative deceleration is set to be a greater value when the above-described difference is great than when the difference is small. Speed-reduction control is performed such that a relative deceleration of the host vehicle with reference to the preceding vehicle is brought close to the target relative deceleration.
Further, known types of travel assist apparatuses include an apparatus that calculates a difference by subtracting a relative deceleration at that time point from the current target relative deceleration at a predetermined interval. The greater the difference, the greater the target relative deceleration at the next time becomes.